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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Topological representations of matroids
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by E. Swartz PDF
J. Amer. Math. Soc. 16 (2003), 427-442 Request permission

Abstract:

There is a one-to-one correspondence between geometric lattices and the intersection lattices of arrangements of homotopy spheres. When the arrangements are essential and fully partitioned, Zaslavsky’s enumeration of the cells of the arrangement still holds. Bounded subcomplexes of an arrangement of homotopy spheres correspond to minimal cellular resolutions of the dual matroid Steiner ideal. As a result, the Betti numbers of the ideal are computed and seen to be equivalent to Stanley’s formula in the special case of face ideals of independence complexes of matroids.
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Additional Information
  • E. Swartz
  • Affiliation: Malott Hall, Cornell University, Ithaca, New York 14853
  • Email: ebs@math.cornell.edu
  • Received by editor(s): August 29, 2002
  • Received by editor(s) in revised form: November 4, 2002
  • Published electronically: November 29, 2002
  • Additional Notes: Partially supported by a VIGRE postdoc under NSF grant number 9983660 to Cornell University
  • © Copyright 2002 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 16 (2003), 427-442
  • MSC (2000): Primary 05B35; Secondary 52C40, 13D02, 13F55
  • DOI: https://doi.org/10.1090/S0894-0347-02-00413-7
  • MathSciNet review: 1949166